KMS Of Academy of mathematics and systems sciences, CAS
| Spectral Method for Phase Retrieval: An Expectation Propagation Perspective | |
| Ma, Junjie1,2,3; Dudeja, Rishabh1; Xu, Ji4; Maleki, Arian1; Wang, Xiaodong2 | |
| 2021-02-01 | |
| Source Publication | IEEE TRANSACTIONS ON INFORMATION THEORY
 |
| ISSN | 0018-9448 |
| Volume | 67Issue:2Pages:1332-1355 |
| Abstract | Phase retrieval refers to the problem of recovering a signal x(star) is an element of C-n from its phaseless measurements y(i) = vertical bar a(i)(H) x(star)vertical bar, where {alpha(i)}(i=1)(m) are the measurement vectors. Spectral method is widely used for initialization in many phase retrieval algorithms. The quality of spectral initialization can have a major impact on the overall algorithm. In this paper, we focus on the model where A = [alpha(1), ... , alpha(m)](H) has orthonormal columns, and study the spectral initialization under the asymptotic setting m, n -> infinity with m/n infinity -> delta is an element of (1, infinity). We use the expectation propagation framework to characterize the performance of spectral initialization for Haar distributed matrices. Our numerical results confirm that the predictions of the EP method are accurate for not-only Haar distributed matrices, but also for realistic Fourier based models (e.g. the coded diffraction model). The main findings of this paper are the following: 1) There exists a threshold on delta(denoted as delta(weak)) below which the spectral method cannot produce a meaningful estimate. We show that delta(weak) = 2 for the column-orthonormal model. In contrast, previous results by Mondelli and Montanari show that delta(weak) = 1 for the i.i.d. Gaussian model. 2) The optimal design for the spectral method coincides with that for the i.i.d. Gaussian model, where the latter was recently introduced by Luo, Alghamdi and Lu. |
| Keyword | Phase measurement Message passing Tools Signal processing algorithms Prediction algorithms Numerical models Approximation algorithms Phase retrieval spectral method coded diffraction pattern expectation propagation (EP) approximate message passing (AMP) state evolution orthogonal AMP vector AMP |
| DOI | 10.1109/TIT.2021.3049172 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | National Science Foundation (NSF)[CCF 1814803] ; Office of Naval Research (ONR)[N000141712827] |
| WOS Research Area | Computer Science ; Engineering |
| WOS Subject | Computer Science, Information Systems ; Engineering, Electrical & Electronic |
| WOS ID | WOS:000612137400036 |
| Publisher | IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/58192 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Ma, Junjie |
| Affiliation | 1.Columbia Univ, Dept Stat, New York, NY 10027 USA 2.Columbia Univ, Dept Elect Engn, New York, NY 10027 USA 3.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China 4.Columbia Univ, Dept Comp Sci, New York, NY 10027 USA |
| Recommended Citation GB/T 7714 | Ma, Junjie,Dudeja, Rishabh,Xu, Ji,et al. Spectral Method for Phase Retrieval: An Expectation Propagation Perspective[J]. IEEE TRANSACTIONS ON INFORMATION THEORY,2021,67(2):1332-1355. |
| APA | Ma, Junjie,Dudeja, Rishabh,Xu, Ji,Maleki, Arian,&Wang, Xiaodong.(2021).Spectral Method for Phase Retrieval: An Expectation Propagation Perspective.IEEE TRANSACTIONS ON INFORMATION THEORY,67(2),1332-1355. |
| MLA | Ma, Junjie,et al."Spectral Method for Phase Retrieval: An Expectation Propagation Perspective".IEEE TRANSACTIONS ON INFORMATION THEORY 67.2(2021):1332-1355. |
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